Bifurcation curves of subharmonic solutions

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure

Social stream classification with emerging new labels

Singapore National Research Foundation under International Research Centres in Singapore Funding Initiativ

Facile Synthesis of High Quality Graphene Nanoribbons

Graphene nanoribbons have attracted attention for their novel electronic and spin transport properties1-6, and because nanoribbons less than 10 nm wide have a band gap that can be used to make field effect transistors. However, producing nanoribbons of very high quality, or in high volumes, remains a challenge. Here, we show that pristine few-layer nanoribbons can be produced by unzipping mildly gas-phase oxidized multiwalled carbon nanotube using mechanical sonication in an organic solvent. The nanoribbons exhibit very high quality, with smooth edges (as seen by high-resolution transmission electron microscopy), low ratios of disorder to graphitic Raman bands, and the highest electrical conductance and mobility reported to date (up to 5e2/h and 1500 cm2/Vs for ribbons 10-20 nm in width). Further, at low temperature, the nanoribbons exhibit phase coherent transport and Fabry-Perot interference, suggesting minimal defects and edge roughness. The yield of nanoribbons was ~2% of the starting raw nanotube soot material, which was significantly higher than previous methods capable of producing high quality narrow nanoribbons1. The relatively high yield synthesis of pristine graphene nanoribbons will make these materials easily accessible for a wide range of fundamental and practical applications.Comment: Nature Nanotechnology in pres

Aharonov-Bohm interferences from local deformations in graphene

One of the most interesting aspects of graphene is the tied relation between structural and electronic properties. The observation of ripples in the graphene samples both free standing and on a substrate has given rise to a very active investigation around the membrane-like properties of graphene and the origin of the ripples remains as one of the most interesting open problems in the system. The interplay of structural and electronic properties is successfully described by the modelling of curvature and elastic deformations by fictitious gauge fields that have become an ex- perimental reality after the suggestion that Landau levels can form associated to strain in graphene and the subsequent experimental confirmation. Here we propose a device to detect microstresses in graphene based on a scanning-tunneling-microscopy setup able to measure Aharonov-Bohm inter- ferences at the nanometer scale. The interferences to be observed in the local density of states are created by the fictitious magnetic field associated to elastic deformations of the sample.Comment: Some bugs fixe

Laser-induced etching of few-layer graphene synthesized by Rapid-Chemical Vapour Deposition on Cu thin films

The outstanding electrical and mechanical properties of graphene make it very attractive for several applications, Nanoelectronics above all. However a reproducible and non destructive way to produce high quality, large-scale area, single layer graphene sheets is still lacking. Chemical Vapour Deposition of graphene on Cu catalytic thin films represents a promising method to reach this goal, because of the low temperatures (T < 900 Celsius degrees) involved during the process and of the theoretically expected monolayer self-limiting growth. On the contrary such self-limiting growth is not commonly observed in experiments, thus making the development of techniques allowing for a better control of graphene growth highly desirable. Here we report about the local ablation effect, arising in Raman analysis, due to the heat transfer induced by the laser incident beam onto the graphene sample.Comment: v1:9 pages, 8 figures, submitted to SpringerPlus; v2: 11 pages, PDFLaTeX, 9 figures, revised peer-reviewed version resubmitted to SpringerPlus; 1 figure added, figure 1 and 4 replaced,typos corrected, "Results and discussion" section significantly extended to better explain etching mechanism and features of Raman spectra, references adde

Disparities and risks of sexually transmissible infections among men who have sex with men in China: a meta-analysis and data synthesis.

BACKGROUND: Sexually transmitted infections (STIs), including Hepatitis B and C virus, are emerging public health risks in China, especially among men who have sex with men (MSM). This study aims to assess the magnitude and risks of STIs among Chinese MSM. METHODS: Chinese and English peer-reviewed articles were searched in five electronic databases from January 2000 to February 2013. Pooled prevalence estimates for each STI infection were calculated using meta-analysis. Infection risks of STIs in MSM, HIV-positive MSM and male sex workers (MSW) were obtained. This review followed the PRISMA guidelines and was registered in PROSPERO. RESULTS: Eighty-eight articles (11 in English and 77 in Chinese) investigating 35,203 MSM in 28 provinces were included in this review. The prevalence levels of STIs among MSM were 6.3% (95% CI: 3.5-11.0%) for chlamydia, 1.5% (0.7-2.9%) for genital wart, 1.9% (1.3-2.7%) for gonorrhoea, 8.9% (7.8-10.2%) for hepatitis B (HBV), 1.2% (1.0-1.6%) for hepatitis C (HCV), 66.3% (57.4-74.1%) for human papillomavirus (HPV), 10.6% (6.2-17.6%) for herpes simplex virus (HSV-2) and 4.3% (3.2-5.8%) for Ureaplasma urealyticum. HIV-positive MSM have consistently higher odds of all these infections than the broader MSM population. As a subgroup of MSM, MSW were 2.5 (1.4-4.7), 5.7 (2.7-12.3), and 2.2 (1.4-3.7) times more likely to be infected with chlamydia, gonorrhoea and HCV than the broader MSM population, respectively. CONCLUSION: Prevalence levels of STIs among MSW were significantly higher than the broader MSM population. Co-infection of HIV and STIs were prevalent among Chinese MSM. Integration of HIV and STIs healthcare and surveillance systems is essential in providing effective HIV/STIs preventive measures and treatments. TRIAL REGISTRATION: PROSPERO NO: CRD42013003721

Molecular Evolution of Ultraspiracle Protein (USP/RXR) in Insects

Ultraspiracle protein/retinoid X receptor (USP/RXR) is a nuclear receptor and transcription factor which is an essential component of a heterodimeric receptor complex with the ecdysone receptor (EcR). In insects this complex binds ecdysteroids and plays an important role in the regulation of growth, development, metamorphosis and reproduction. In some holometabolous insects, including Lepidoptera and Diptera, USP/RXR is thought to have experienced several important shifts in function. These include the acquisition of novel ligand-binding properties and an expanded dimerization interface with EcR. In light of these recent hypotheses, we implemented codon-based likelihood methods to investigate if the proposed shifts in function are reflected in changes in site-specific evolutionary rates across functional and structural motifs in insect USP/RXR sequences, and if there is any evidence for positive selection at functionally important sites. Our results reveal evidence of positive selection acting on sites within the loop connecting helices H1 and H3, the ligand-binding pocket, and the dimer interface in the holometabolous lineage leading to the Lepidoptera/Diptera/Trichoptera. Similar analyses conducted using EcR sequences did not indicate positive selection. However, analyses allowing for variation across sites demonstrated elevated non-synonymous/synonymous rate ratios (dN/dS), suggesting relaxed constraint, within the dimerization interface of both USP/RXR and EcR as well as within the coactivator binding groove and helix H12 of USP/RXR. Since the above methods are based on the assumption that dS is constant among sites, we also used more recent models which relax this assumption and obtained results consistent with traditional random-sites models. Overall our findings support the evolution of novel function in USP/RXR of more derived holometabolous insects, and are consistent with shifts in structure and function which may have increased USP/RXR reliance on EcR for cofactor recruitment. Moreover, these findings raise important questions regarding hypotheses which suggest the independent activation of USP/RXR by its own ligand

Observation of the electromagnetic doubly OZI-suppressed decay J/ψ→ϕπ0J/\psi \rightarrow \phi \pi^{0}

Using a sample of $1.31$ billion $J/\psi$ events accumulated with the BESIII detector at the BEPCII collider, we report the observation of the decay $J/\psi \rightarrow \phi\pi^{0}$, which is the first evidence for a doubly Okubo-Zweig-Iizuka suppressed electromagnetic $J/\psi$ decay. A clear structure is observed in the $K^{+} K^{-}$ mass spectrum around 1.02 GeV/$c^2$, which can be attributed to interference between $J/\psi \rightarrow \phi\pi^{0}$ and $J/\psi \rightarrow K^{+}K^{-}\pi^{0}$ decays. Due to this interference, two possible solutions are found. The corresponding measured values of the branching fraction of $J/\psi \to \phi\pi^{0}$ are $[2.94 \pm 0.16\text{(stat.)} \pm 0.16\text{(syst.)}] \times 10^{-6}$ and $[1.24 \pm 0.33\text{(stat.)} \pm 0.30\text{(syst.)}] \times 10^{-7}$.Comment: 7 pages, 4 figures, published in Phys. Rev.

Abnormal behavior of the optical potential for the halo nuclear system <font size=-1>⁶</font>He+<font size=-1>²⁰⁹</font>Bi

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